Inverse Design of Photonic Surfaces via High throughput Femtosecond Laser Processing and Tandem Neural Networks

Abstract This work demonstrates a method to design photonic surfaces by combining femtosecond laser processing with the inverse design capabilities of tandem neural networks that directly link laser fabrication parameters to their resulting textured substrate optical properties. High throughput fabrication and characterization platforms are developed that generate a dataset comprising 35280 unique microtextured surfaces on stainless steel with corresponding measured spectral emissivities. The trained model utilizes the nonlinear one‐to‐many mapping between spectral emissivity and laser parameters. Consequently, it generates predominantly novel designs, which reproduce the full range of spectral emissivities (average root‐mean‐squared‐error < 2.5%) using only a compact region of laser parameter space 25 times smaller than what is represented in the training data. Finally, the inverse design model is experimentally validated on a thermophotovoltaic emitter design application. By synergizing laser‐matter interactions with neural network capabilities, the approach offers insights into accelerating the discovery of photonic surfaces, advancing energy harvesting technologies.

In the context of training an inverse deep neural network (DNN), challenges arise when it is not incorporated within the tandem neural network (TNN) framework.These challenges stem primarily from the problem's inherent one-to-many mapping nature.While the objective during DNN training is to minimize the loss function and fine-tune the weights, an intriguing observation emerges; even if the predicted emissivity (highlighted in red) closely aligns with the true emissivity, there may remain a significant difference between the true and predicted parameters.This disparity is largely due to the one-to-many relationships involved.Incorporating a trained forward DNN into the TNN framework addresses this challenge.By using an outer loss function to compare the true and predicted emissivity curves, the inverse DNN can be more accurately calibrated.The emission powers and associated figure of merits (FOMs) are calculated by integrating the emissivity, weighted by a Plank distribution at 1400 K, from zero microns up to the bandgap for in-band emission, and from the bandgap out to 12 µm wavelength for the out-of-band emissions.Specifically, weighted thermal emission,  (, ) , can be calculated based on Planck's blackbody radiation, as expressed below.
where, () is the spectral emissivity, ℎ is the Planck's constant,  is the speed of light,  is the wavelength,   is the Boltzmann constant, and  is the temperature of 1400 K.

Figure S1 .
Figure S1.Schematic of ultrafast fs laser processing with a raster scanning method.Three different laser parameters including laser power, scanning speed, and spacing are used to texture the target surface area.Using variables as parameter inputs, a total of 35,280 different surfaces were generated.

Figure S2 .
Figure S2.Schematic of the custom Fourier Transform Infrared spectrometer (FTIR) microscope system.A reflective objective lens was used to focus the IR beam on the target surface.To achieve high signal to noise ratios for acquired data, a liquid-nitrogen cooled Mercury-Cadmium-Telluride detector was coupled with the FTIR.LabVIEW software was used to synchronize the FTIR equipment and motorized stages for automated high throughput optical property measurements.

Figure S3 .
Figure S3.Examples of spectral emissivity of photonic structures laser-fabricated on stainless steel by changing the laser power while maintaining the same spacing of 16 μm and speed of 10 mm/s.

Figure S4 .
Figure S4.Average emissivity of 35,280 photonic surfaces fabricated on stainless steel under different laser processing conditions.

Figure S5 .
Figure S5.Average emissivity distribution of 35,280 photonic surfaces as a function of power, spacing, and speed, respectively.

Figure S6 .
Figure S6.The schematic representation of one-to-many mapping in inverse design.

Figure S7 .
Figure S7.The experimental emissivity curves (N = 3,038) that correspond to the test set laser parameters presented in Fig. 3b.

Figure S10 .
Figure S10.Partial dependence plot of spectral emissivity with respect to the speed and the spacing at the fixed power of (a) 0.2 W, (b) 0.6 W, and (c) 1.3 W, respectively.

Figure S11 .
Figure S11.Partial dependence plot of spectral emissivity with respect to the speed and the power at the fixed spacing of (a) 2 µm, (b) 21 µm, and (c) 42 µm, respectively.

Figure S12 .
Figure S12.Partial dependence plot of spectral emissivity with respect to the power and the spacing at the fixed speed of (a) 10 mm/s, (b) 100 mm/s, and (c) 350 mm/s, respectively.

Figure S13 .
Figure S13.Weighted thermal emission and spectral emissivity for (a) 100% model, (b) 90% model, and (c) 70% model, respectively.Representative laser parameters for each model are listed as inset numbers.

Table S2 .
Laser processing parameters predicted by the trained Inverse DNN models for the TPV ideal emissivity target shown in Fig.4d.